The present invention pertains generally to devices and methods for chemical separation. More particularly, the present invention pertains to devices and methods for the extraction of sodium from sodium compounds. The present invention is particularly, but not exclusively, useful for recovering sodium hydride from a mixture of methane and sodium hydroxide.
Recently, there has been an abundant interest in the use of sodium hydride (NaH) as a portable energy source to produce hydrogen as a replacement for fossil fuels such as gasoline. For example, engines similar to the standard gasoline engines that are now used in automobiles can be manufactured that use hydrogen gas as a fuel. Unfortunately, the bulk amount of actual hydrogen gas that is needed for vehicle applications would require either an extremely large tank or a high-pressure vessel. Both of these requirements can be expensive and impractical for use on a vehicle. Thus, to avoid these requirements, devices have been proposed to produce hydrogen gas at relatively low pressures. Importantly, the gas can be produced as demanded by the hydrogen engine, by reacting sodium hydride with water according to the reaction:
NaH+H2ONaOH+H2xe2x80x83xe2x80x83(Reaction 1) 
For example, U.S. Pat. No. 5,728,464 entitled xe2x80x9cHydrogen Generation Pelletized Fuelxe2x80x9d which issued to Checketts on Mar. 17, 1998 discloses sodium hydride pellets for a hydrogen demand system. Specifically, Checketts discloses sodium hydride pellets that are coated with a water impervious barrier. The barrier can be removed either mechanically or electrically to expose the sodium hydride core for reaction with water to produce hydrogen.
As indicated by Reaction 1 above, a by-product of the reaction is sodium hydroxide (NaOH). It has been proposed elsewhere to recover sodium hydride (NaH) from the by-product sodium hydroxide (NaOH) by heating the sodium hydroxide (NaOH) in a methane (CH4) atmosphere. Specifically, at a reaction temperature of approximately 900 C (1173 K), the reaction:
NaOH+CH4CO+2.5H2+Na(g)xe2x80x83xe2x80x83(Reaction 2) 
can be used to produce sodium gas Na(g). Unfortunately, when the hot, reaction products of Reaction 2 are sent to a cold collector under modest pressures, sodium hydroxide (NaOH) rather than liquid sodium Na(l) condenses on the collector. Specifically, in accordance with the following analysis, pressures exceeding approximately 4200 atmospheres are required to condense liquid sodium Na(l) rather than sodium hydroxide (NaOH) on the cold collector.
Before concluding that impractical pressures are required to condense liquid sodium, attempts to shift the equilibrium by introducing other compounds into the mixture were considered. After consideration, this approach appears to be futile. Specifically, the following compounds (all in the gas phase) have been considered; H, Na, O, Na+, H2, O2, OH, NaH, CO, NaO, NaOH, CO2, H2O, H2CO, CH4. Carbon has very low vapor pressure and, therefore, carbon vapor has been excluded from the above list. FIG. 1 shows the concentrations of the different compounds as a function of temperature at a total pressure of 1 atm. FIG. 1 was obtained theoretically by minimizing free energy and using balance equations for the different elements. Compounds having a concentration less then 10xe2x88x928 are not shown.
Referring to FIG. 1, it can be seen that at low temperatures, T less than 600 K, the major components are NaOH and CH4. In the temperature range, 1000 K less than T less than 2000 K, the major compounds are indeed CO, H2, and Na vapor as predicted by Reaction 2. At T greater than 3000 K, Na becomes ionized and H2 molecules dissociate. The other compounds considered and listed above are not essential. Atomic and molecular oxygen is not present in the full temperature range. Therefore, at low temperatures, when Na is not ionized and hydrogen is in molecular form, a simple model based on Reaction 2 can be used. The partial pressures of methane, carbon monoxide and hydrogen can be expressed in terms of the partial pressures of NaOH and Na, using Reaction 2 as follows:
pCH4=pNaOH, pCO=pNa, pH2=2.5pNaxe2x80x83xe2x80x83(eq. 1) 
As such, the total pressure will be:
p=pNaOH+pCH4+pNa+pCO+pH2=4.5pNa+2pNaOHxe2x80x83xe2x80x83(eq. 2) 
Thus, the equilibrium equation for Reaction 2 can be written as follows:
(pNapCOpH22.5)/(pNaOHpCH4)=K(T) 
or using equation (1):
2.52.5pNa4.5/pNaOH2=K(T)xe2x80x83xe2x80x83(eq. 3) 
Equations 2 and 3 allow the partial pressures of Na and NaOH to be evaluated as function of total pressure, p, and temperature, T. Thus, the full model revealed by FIG. 1 comports closely with the simple model (Reaction 2) at low temperatures, T less than 2000 K. Further, equations 2 and 3 show that at higher pressures, higher temperatures are required to reduce sodium.
Next, an analysis can be conducted to determine the temperature range in which the gaseous model is valid. Specifically, the gaseous model is valid when the partial pressures of Na or NaOH are less then the saturated pressures for these compounds. The other major compounds such as H2, CO and CH4 have very high vapor pressures, and accordingly, do not condense. FIG. 2 shows the saturated pressure to partial pressure ratios for the case presented in FIG. 1. It can be seen that at a total pressure of p=1 atm, the condensation point (psat=p) for NaOH occurs at a higher temperature than for Na. Thus, at this pressure, Na will be collected in the form of NaOH rather then metallic Na. An increase in the total pressure can shift the reaction and in principle can create a condition where Na has a condensation point at a higher temperature than NaOH. The total pressure necessary to condense Na rather than NaOH can be derived from equation 3 by replacing the partial pressures of each constituent by their corresponding saturated pressures:
2.52.5ps,Na4.5/psNaOH2 less than K(T) 
The above condition is satisfied at T greater than 3000 K and a total pressure of approximately:
p greater than 4.5ps,Na+2ps, NaOH=4200atm 
which is simply not practical. Thus, the above analysis indicates that at moderate pressures, the equilibrium condensation of Na does not take place.
The present invention contemplates separation of Na from the other gases by ionization. For example, consider a mixture of NaOH and CH4 heated to a temperature of 3000-4000 K rather than to 1000 K. This heating can be accomplished using a plasma torch. At these higher temperatures, Na atoms will be fully ionized. The present invention further contemplates separating the ionized Na component from the non-ionized neutrals (i.e. CO and H2) by introducing the mixture in the form of a plasma jet into a strong magnetic field. In the magnetic field that is directed along the jet, sodium ions will move predominantly along the magnetic field lines and neutrals will diffuse from the plasma jet radially, where the neutrals can be pumped from the device. As such, an increase of sodium concentration along the plasma jet can be expected. Specifically, the following analysis estimates the increase in sodium concentration along the plasma jet.
First, consider a comparison between the magnetic pressure and the gas pressure. Magnetic pressure, pm, can be found using the equation:
pm=B2/8xcfx80, 
or in practical units
pm[Pa]=BG2/80xcfx80. 
For example, for B=3 kG, pm=3.6 104 Pa=270 Torr which is larger then the expected gas pressure in the plasma jet, p=1-5 kPa. To derive the radial velocities of the neutrals, ions, and electrons, momentum balance equations for these particles with friction forces acting between different components can be considered. Assuming a cylindrical plasma jet in a uniform axial magnetic field, the result is:
Vri=Vre=xe2x88x92(c/eB)2(dpxcexa3/dr)(xcexci0xcexce0Ki0Ke0n0/ni/(xcexci0Ki0+xcexce0Ke0)+xcexceiKei)xe2x80x83xe2x80x83(eq. 4) 
and 
Vr0=Vrixe2x88x92(dp0/dr)/(xcexci0Ki0+xcexce0Ke0)/ni/n0xe2x80x83xe2x80x83(eq. 5) 
where pxcexa3 is total pressure of all components, xcexcij=MiMj/(Mi+Mj) and the K""s are collision rates. In equation 5, xcexce0Ke0 less than  less than xcexci0Ki0 and can be neglected. It can be seen that the plasma radial velocity can be made small by increasing the magnetic field. As one can expect, the separation of neutrals is driven by neutral pressure. Equation 5 is valid when the plasma density is high and the neutral""s mean free path before collision with ions is smaller than the jet radius. In terms of plasma density, this condition is fulfilled for a jet with radius, a=cm, when nixe2x89xa71020 mxe2x88x923, or pxe2x89xa73 Pa, both of which are valid for the plasma jets of interest considered below.
Plasma diffusion across a magnetic field is generally anomalous, and accordingly, instead of using equation 4, the radial plasma velocity can be used as a parameter. As such, the radial expansion of the plasma jet can be described by the following:
a(x)=a0+(Vr/Vx)x. 
Here, x is the coordinate along the jet and ao is the initial radius of the jet. It is also assumed that the axial velocity of the jet is independent of x. In this approximation, plasma density can be described by the following equation:
dGi/dx=xe2x88x92xcfx80a2Kr(T)ni3xe2x80x83xe2x80x83(eq. 6) 
Here, Gi=xcfx80a2Vxni and Kr is a three-body recombination coefficient. Further, the dependence of Kr on T can be derived from Voronov""s ionization rate (see for example, G. S. Voronov, Atomic Data and Nuclear Data Tables, Vol. 65, No. 1, January, 1997) and the Saha equilibrium for sodium ions. Temperature scaling for Kr is:
Kr=6.5 10xe2x88x9241(5800/TK)1.15. 
It is assumed that sodium neutrals escape from the plasma jet and, therefore, equation 6 describes the decrease of sodium flux along the plasma jet.
Using equation 5, one can derive an equation for the neutral flux in the jet:
dG0/dx=xe2x88x922G0T0/(xcexci0Ki0niVxa2)xe2x80x83xe2x80x83(eq. 7) 
where G0=xcfx80a2Vxn0. Equation (7) allows estimation of the required length of the jet:
L=xcexci0Ki0Gi/2xcfx80T0. 
It can be seen that the separation length does not depend on the jet radius or jet density but only on the ion throughput and the gas temperature. For example, for a Hydrogen and CO mixture, with T0=2000:
L(m) greater than 30Gi(mol/s) 
In a device with an axial length, Lxcx9c1 m, the throughput should not exceed 10xe2x88x922 mol/s for a good separation. Separation can be affected by recombination of the Sodium ions. Recombination length can be estimated from equation 6:
L=Vx/Krni2. 
For example, at Lxcx9c1 m and T=2000 K, recombination is small when ni less than 2 1021 mxe2x88x923 (i.e. total density n less than 9 1021 mxe2x88x923) or when plasma pressure in the jet is less then approximately 250 Pa. At a higher pressure, recombination can significantly reduce the separation of sodium.
To better estimate this effect, equations 6 and 7 can be solved together with power balance equations for ions and neutrals:
3ni{fraction (5/3)}VxdSi/dx=(2Ti+Eiz)Krni3xe2x88x92Pradxe2x88x92Ki0nin0(Tixe2x88x92T0) 
1.5n0{fraction (5/3)}VxdS0/dx=Ki0nin0(Tixe2x88x92T0)xe2x88x92k(T0xe2x88x92Tout)a2 
where S=T/n⅔. The radiation power has been estimated for a single sodium line. FIG. 3 shows the plasma and gas pressures, and FIG. 4 shows the temperatures as a function of distance from the nozzle. It can be seen that Ti is very close to T0 inside the plasma jet. Gas temperature outside the plasma jet, Tout, decreases much faster due to adiabatic expansion of the gas. It was assumed that neutral gas can freely expand outside the jet. In this case the gas pressure in the jet is also much higher then the ambient pressure. FIG. 5 shows the throughput of sodium ions (GNa) and CO neutrals (GNaOH). Presence of CO will cause condensation of NaOH during thermal quench on a cold collector and should be minimized. It can be seen that at L=0.5 m, sodium throughput is about 3 times larger then CO throughput and, therefore NaOH impurity will be about 30% in this particular case. However, this fraction is sensitive to the divergence of the jet. For example, fraction of NaOH decreases to only 1% at zero divergence of the jet, Vr=0. If initial pressure is small (i.e. p less than 2000) then the recombination effect is not very important. At higher pressures, the recombination effect can be significant.
Faster cooling of the jet also reduces separation because lower temperatures increase the recombination of sodium ions and reduce the radial diffusion of neutrals from the jet. An example of fast jet cooling (black body radiation) is shown in FIGS. 7 and 8.
The negative effects of jet divergence, ion recombination, and cooling of the jet on the ion separation can be reduced if a radial electric field is applied to the plasma jet. The electric field can be applied, for example, by installing ring electrodes in the separation chamber and biasing these electrodes in such a manner that an electric field with a desirable radial profile will be set up. Due to the large electrical conductance of the plasma along the magnetic field lines, the radial electric field will exist in the full volume of the chamber. By directing the electric field inwardly, the ions will be restrained from radial expansion.
The crossed radial electric and magnetic fields will cause ion and electron rotation with azimuthal velocity VE=E/B. The azimuthal friction force between rotating ions and slower rotating neutrals will result in an inward ion drift. As a result, the jet diffusive expansion will be suppressed. Because electrons cannot move in the radial direction, radial current will flow in the plasma. This current is supplied by the ring electrodes. Obviously, the electric field will only propagate from the electrodes to the plasma volume if the electrical conductivity along the magnetic field lines is larger than the electrical conductivity across the magnetic field in the radial direction. Stated another way, the voltage drop along the field lines has to be much smaller than the voltage drop across the field lines,
U∥/Ur=2(L/a)2("sgr"r/"sgr"∥) less than  less than 1.xe2x80x83xe2x80x83(eq. 8) 
Radial electrical conductivity, "sgr"r, can be estimated with the help of an azimuthal momentum balance of ions and neutrals,
0=xcexci0Ki0n0ni(Vxcex80xe2x88x92Vxcex8i)+xcexd0d2Vxcex80/dr2xe2x80x83xe2x80x83(eq. 9) 
0=eniVriB/c+xcexci0Ki0n0ni(Vxcex80xe2x88x92Vxcex8i).xe2x80x83xe2x80x83(eq. 10) 
The viscous force can be estimated by replacing d2Vxcex80/dr2 with 2Vxcex80/a2, and representing neutral viscosity as xcexd0=n0m0Vth0/3a(a/xcex0+1). The viscosity has been corrected to extend momentum loss on low density xcex0/a greater than 1. Radial electrical conductance can be derived from the above equations:
"sgr"r=jr/Er=(2e2ni/mcxcfx89e)(m0/mi)(no/ni)(Vth0/3xcfx89ia)/(1+a/xcex0+2m0Vth0/3axcexci0Ki0ni)xe2x80x83xe2x80x83(eq. 11) 
where xcfx89e=eB/mec, and xcex0 is the neutral atom mean free path. Parallel electrical conductivity can be described by the well known classical approximation,
"sgr"∥=2nie2xcfx84e/me.xe2x80x83xe2x80x83(eq. 12) 
Equation 8 can be combined with equations 11 and 12 to yield:
xcfx89excfx84e greater than  greater than (⅔)(L/a)2(m0/mi)(n0/ni)(Vth0/xcfx89ia)/(1+a/xcex0+2m0Vth0/3axcexci0Ki0ni).xe2x80x83xe2x80x83(eq. 13) 
Because xcfx89e,ixcx9cB and xcfx84excx9c1/ni, the last equation allows estimation of the minimum magnetic field for a given plasma density that is needed for propagation of electric field from the electrodes to the plasma. It is well known that the radial field cannot only compress the plasma jet but can also heat the ion component to a temperature, Ti,
Ti=miVE2/3xe2x80x83xe2x80x83(eq. 14) 
The ions, in turn, will heat the neutral components and electrons, speeding up the diffusion of neutrals from the plasma jet. Higher temperatures will reduce the recombination of the Na ions. For example, at a magnetic field B=3 kG and jet radius of a=5 cm, the ion density can be as high as ni=1021mxe2x88x923 (U∥/Urxcx9c0.1) The required voltage is about 100V. At this voltage the ion temperature in the jet will be about 2-3 eV, and radial contraction of the jet due to the radial electric field is Vr/V∥xcx9c0.05. The ion Larmor radius is about 4 mm and, hence, ten ring electrodes are sufficient to control the radial profile of electric field. A jet length of L=1 m is sufficient to remove most of the neutrals by differential pumping. Ion throughput is about G=0.07 mol/s.
Thus in accordance with the analysis set forth above, a separation device with axial length of about 1 m can produce about 0.1-0.2 g of sodium per second. Excessive recombination in the plasma jet and plasma cooling can be avoided by applying an inwardly radial electric field, Vxcx9c100V. Although the separation of Na from NaOH is not perfect, an NaOH impurity of only about 5%-10% can be expected on the collector.
In light of the above, it is an object of the present invention to provide devices and methods suitable for the purposes of extracting liquid sodium (Na) from a material containing sodium compounds such as sodium hydroxide (NaOH). It is another object of the present invention to provide devices and methods for producing sodium hydride from a mixture of sodium hydroxide (NaOH) and methane (CH4). Yet another object of the present invention is to provide devices and methods for producing sodium hydride which are easy to use, relatively simple to implement, and comparatively cost effective.
The present invention is directed to a device and method for producing sodium from a feed material that contains sodium compounds. For example, a mixture of methane (CH4) and sodium hydroxide (NaOH) is suitable for use as a feed material in the device and methods of the present invention to produce sodium. Once the sodium is extracted from the feed material in accordance with the present invention, it can be mixed with hydrogen gas to form sodium hydride (NaH). As described above, sodium hydride (NaH) is useful as an alternative energy source, because hydrogen gas is generated when sodium hydride (NaH) is mixed with water.
For the present invention, a plasma torch is configured to heat the feed material to a temperature sufficient to reduce and ionize sodium (Na). As such, the plasma torch creates a plasma jet containing ionized sodium (Na). For a feed material such as the methane (CH4) and sodium hydroxide (NaOH) combination described above, a temperature above 2000 degrees C. is sufficient to reduce and ionize sodium. At this temperature, other molecules created in the plasma jet, such as hydrogen (H) and carbon monoxide (CO), will remain as non-ionized neutrals.
From the plasma torch, the plasma jet is introduced into a chamber where a magnetic field has been established. Preferably, the chamber is surrounded by a wall shaped as an elongated cylinder. The wall defines a longitudinal axis and is formed with a first end and a second end. The cylindrical wall is preferably open at both ends, allowing particles to enter the chamber at the first end and exit the chamber at the second end. To establish the magnetic field inside the chamber, standard coils can be mounted on the outside of the wall, and an electrical current can be selectively passed through the coils. Preferably, the magnetic field established inside the chamber is oriented substantially parallel to the longitudinal axis. Further, the magnetic field is preferably established having a substantially uniform field strength along the longitudinal axis. In accordance with the present invention, an optional ring electrode can be positioned in the chamber near the second end to establish an inwardly directed electric field in the chamber. As explained above, the inwardly directed electric field can reduce the negative effects of jet divergence, ion recombination and cooling of the jet.
For the present invention, the first end of the cylindrical wall is positioned adjacent the plasma torch to allow the plasma jet that is created by the plasma torch to be directed into the chamber. Once inside the chamber, the heated mixture of ions and neutrals interacts with the magnetic field in the chamber to cause the sodium ions to travel along the magnetic field lines. Thus, the sodium ions enter the chamber at the first end, travel on paths substantially parallel to the longitudinal axis and exit the chamber at the second end. On the other hand, the neutrals are essentially unaffected by the magnetic field. As such, the neutrals are able to travel in directions that extend away from the longitudinal axis.
A collector plate is positioned near the second end of the cylindrical wall to receive and accumulate sodium (Na). The cylindrical wall is further formed with an outlet near its first end to pass neutrals from the chamber to a secondary processing tank. Conventional techniques can be used at the secondary processing tank to separate hydrogen gas from any other gasses present. If desired, the accumulated sodium from the collector plate can be combined with the gaseous hydrogen from the secondary processing tank to form sodium hydride (NaH).